On the boundedness of hyperbolic Riesz B-potential

详细信息    查看全文

• 作者：Elina L. Shishkina
• 关键词：hyperbolic Riesz B ; potential ; fractional power of singular hyperbolic operator ; Lorentz distance ; singular Bessel differential operator ; generalized translation ; Marcinkiewicz interpolation theorem ; bounded operator
• 刊名：Lithuanian Mathematical Journal
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：56
• 期：4
• 页码：540-551
• 全文大小：263 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Statistics
  Algebra
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-8825
• 卷排序：56

文摘

This paper deals with the hyperbolic Riesz B-potential, which is the negative real power of an operator B_γ1 − ∑_i = 2nB_γi, where \( \begin{array}{cc}\hfill {B}_{\upgamma i}={\partial}^2/\partial {x}_i^2+\left({\upgamma}_i/{x}_i\right)\partial /\partial {x}_i,\hfill & \hfill i=1,\dots, n,\hfill \end{array} \) is a singular Bessel differential operator. We prove the boundedness of the hyperbolic Riesz B-potential in proper spaces.